SOLUTION: 2 times sq. root of x minus sq. root of 2x+1=1

Algebra ->  Radicals -> SOLUTION: 2 times sq. root of x minus sq. root of 2x+1=1      Log On


   

Question 102403This question is from textbook
: 2 times sq. root of x minus sq. root of 2x+1=1 This question is from textbook

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2sqrt(x)-sqrt(2x+1)=1
2sqrt(x)-1=sqrt(2x+1)
4x-4sqrt(x)+1=2x+1 square both sides
-4sqrt(x)=-2x subtract 4x+1 from each side.
16x=4x^2 square both sides
4x^2-16x=0 subtract 16x from each side.
4x(x-4)=0 factor
x=0, x=4
Check:
2sqrt(0)-sqrt(0+1)=1...-1=1 false so x=0 is not an answer.
2sqrt(4)-sqrt(2*4+1)=1...2*2-3=1 true so x=4 is the only answer.
Ed